Rafter Geometry Formulas
\(\text{Adjusted Run (ft)} = \text{Roof Run (ft)} - \left(\frac{\text{Ridge Thickness (in)} / 2}{12}\right)\) \(\text{Roof Rise (ft)} = \text{Adjusted Run (ft)} \times \left(\frac{\text{Pitch}}{12}\right)\) \(\text{Common Rafter Length (ft)} = \sqrt{\text{Adjusted Run}^2 + \text{Roof Rise}^2}\) \(\text{Pitch Factor} = \sqrt{1 + \left(\frac{\text{Pitch}}{12}\right)^2}\) \(\text{Overhang Length (ft)} = \left(\frac{\text{Overhang Run (in)}}{12}\right) \times \text{Pitch Factor}\) \(\text{Total Rafter Length (ft)} = \text{Common Rafter Length} + \text{Overhang Length}\) \(\text{Pitch Angle } (\theta) = \arctan\left(\frac{\text{Pitch}}{12}\right) \times \frac{180}{\pi}\)
Rafter Length Reference Table (12 ft Building Span / 6 ft Run)
| Roof Pitch | Roof Angle (°) | Pitch Multiplier | Common Rafter Length (6’ Run) | 12” Overhang Tail | Total Rafter Length | Stock Board Size |
|---|---|---|---|---|---|---|
| 4/12 Pitch | 18.43° | 1.054 | 6.27 ft (75.3”) | 1.05 ft | 7.32 ft | 8 Foot Board |
| 6/12 Pitch | 26.57° | 1.118 | 6.66 ft (79.9”) | 1.12 ft | 7.78 ft | 8 Foot Board |
| 8/12 Pitch | 33.69° | 1.202 | 7.15 ft (85.8”) | 1.20 ft | 8.35 ft | 10 Foot Board |
| 10/12 Pitch | 39.81° | 1.302 | 7.75 ft (93.0”) | 1.30 ft | 9.05 ft | 10 Foot Board |
| 12/12 Pitch | 45.00° | 1.414 | 8.42 ft (101.0”) | 1.41 ft | 9.83 ft | 10 Foot Board |
How to Use This Rafter Length Calculator
- Input total horizontal Roof Run in feet (half the building span for gable roofs).
- Enter Roof Pitch (inches of rise per 12 inches of horizontal run).
- Specify Ridge Beam Thickness (1.5” standard for 2x dimensional ridge board).
- Enter horizontal Overhang Run in inches (e.g., 12” soffit).
- Review exact common rafter length, overhang tail length, total rafter length, slope angle, and stock lumber purchasing size.
Frequently Asked Questions
What is the formula for calculating rafter length?
Rafter length is calculated using the Pythagorean theorem: Rafter Length = √(Adjusted Run² + Total Rise²), where Adjusted Run = Roof Run - (Half Ridge Thickness / 12) and Total Rise = Adjusted Run × (Pitch / 12).
What is roof run?
Roof run is the horizontal distance from the outer edge of the wall plate to the center of the roof ridge beam. For a symmetrical gable roof, run equals half the total building width.
Why must you deduct ridge board thickness from rafter length?
Rafters meet at the center of the roof against a ridge beam. Deducting half the thickness of the ridge beam (0.75” for a 1.5” 2x board) ensures the rafter plumb cut fits tight against the ridge.
How do you calculate rafter overhang?
Overhang length equals (Horizontal Overhang in feet) × √(1 + (Pitch / 12)²). For a 12-inch overhang on a 6/12 pitch roof, the rafter tail length is 1.118 feet (13.4 inches).
What size lumber should I purchase for rafters?
Always round up to the next standard commercial board length (e.g., 8’, 10’, 12’, 14’, 16’, 18’, 20’) to allow for bird’s mouth plumb cuts and fascia trimming.
How do you convert pitch to degrees?
Pitch angle in degrees = arctan(Pitch / 12) × (180 / π). For example, a 6/12 pitch equals arctan(0.5) = 26.57 degrees.
Is my rafter framing calculation saved on external servers?
No. All calculation logic executes locally in your browser.